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arXiv · 1102.4609

Generalising the logistic map through the $q$-product

Robson W. S. Pessoa·Ernesto P. Borges
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Abstract

We investigate a generalisation of the logistic map as $ x_{n+1}=1-ax_{n}\otimes_{q_{map}} x_{n}$ ($-1 \le x_{n} \le 1$, $0 1$ at the edge of chaos, particularly at the first critical point $a_c$, that depends on the value of $q_{map}$. Bifurcation diagrams, sensitivity to initial conditions, fractal dimension and rate of entropy growth are evaluated at $a_c(q_{map})$, and connections with nonextensive statistical mechanics are explored.

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Robson W. S. Pessoa, Ernesto P. Borges. 2011-02-22. Generalising the logistic map through the $q$-product. https://doi.org/10.1088/1742-6596%2F285%2F1%2F012042

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